Convex Optimization for Aerospace Guidance and Control Applications

A special issue of Aerospace (ISSN 2226-4310).

Deadline for manuscript submissions: closed (9 June 2023) | Viewed by 6369

Special Issue Editor


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Guest Editor
Department of Mechanical and Aerospace Engineering, Sapienza University of Rome, Via Eudossiana 18, 00184 Rome, Italy
Interests: optimal control; trajectory optimization; attitude control; ascent trajectory; rocket control; convex optimization; reinforcement learning
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Special Issue Information

Dear Colleagues,

The increasing number of commercial applications in the aeronautic segment and the proposals of ambitious programs by national space agencies are boosting the rise of autonomous aerospace systems. A growing number of future spacecraft (S/C) are expected to operate autonomously in highly uncertain environments to enable novel mission concepts, while on Earth, unmanned aerial vehicles (UAVs) will be tasked with operating autonomously in complex and overpopulated urban environments to deliver commercial goods or emergency medical supplies, monitor traffic, etc., while avoiding collisions and granting the maximum economical return. The capability of designing a safe yet optimal control policy under significant uncertainty is thus paramount. Traditional optimal control methods based on direct or indirect methods represent consolidated tools to plan a deterministic trajectory, but a significant leap is expected to be taken in the next few years to address the forthcoming challenges in terms of performance, trustworthiness, and safety.

Convex optimization has increasingly gained popularity among the aerospace community in the last several decades, overcoming traditional methods for the solution of optimal control problems. The main factors driving this trend have been the availability of powerful interior-point algorithms for the solution of convex problems in polynomial time, theoretically sound proofs of convergence, and the rise of convexification techniques that make it possible to solve originally nonlinear problems through convex optimization algorithms. When paired with model predictive control (MPC), convex optimization makes it possible to set up a computationally efficient real-time guidance framework capable of ensuring that the flight trajectory will respect all mission constraints, be robust to model uncertainties and external disturbances, and maximize the mission performance.

This Special Issue intends to bring recognition to significant trends and novel applications of convex optimization in the field of the guidance and control of aerospace systems. Despite all these advances, several topics remain under investigation. A first area of interest concerns the development of novel lossless or successive convexification techniques to enable and expand the classes of problems that can be solved by convex optimization. A second area of interest concerns the investigation of modern and efficient discretization strategies that allow for accounting for bang–off–bang control structures. Third, reports and analyses of hardware-in-the-loop and in-flight tests that confirm the validity of embedded convex solutions for computational guidance would greatly increase the attention of private companies toward this topic.

This Special Issue thus welcomes all contributions willing to apply convex optimization methodology to aerospace problems in areas including but not limited to:

  • Ascent trajectory optimization;
  • Space trajectory optimization;
  • Reusable launch vehicle landing;
  • Spacecraft hypersonic reentry;
  • Planetary or asteroid landing trajectories;
  • Spacecraft rendezvous and docking;
  • Drone and UAV trajectories;
  • Path planning for fixed-wing and quadrotor vehicles;
  • Landing and/or take-off runway optimization;
  • Robotic devices for exploration;
  • Ad-hoc methods for solving convex problems in real-time applications.

Dr. Alessandro Zavoli
Guest Editor

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Aerospace is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • convex optimization
  • optimal control
  • space trajectory
  • obstacle avoidance
  • ascent trajectory
  • path planning
  • urban air mobility

Published Papers (3 papers)

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17 pages, 435 KiB  
Article
A Geometrical, Reachable Set Approach for Constrained Pursuit–Evasion Games with Multiple Pursuers and Evaders
by Olli Jansson and Matthew W. Harris
Aerospace 2023, 10(5), 477; https://doi.org/10.3390/aerospace10050477 - 18 May 2023
Cited by 1 | Viewed by 1407
Abstract
This paper presents a solution strategy for deterministic time-optimal pursuit–evasion games with linear state constraints, convex control constraints, and linear dynamics that is consistent with linearized relative orbital motion models such as the Clohessy–Wiltshire equations and relative orbital elements. The strategy first generates [...] Read more.
This paper presents a solution strategy for deterministic time-optimal pursuit–evasion games with linear state constraints, convex control constraints, and linear dynamics that is consistent with linearized relative orbital motion models such as the Clohessy–Wiltshire equations and relative orbital elements. The strategy first generates polytopic inner approximations of the players’ reachable sets by solving a sequence of convex programs. A bisection method then computes the optimal termination time, which is the least time at which a set containment condition is satisfied. The pursuit–evasion games considered are games with (1) a single pursuer and single evader, (2) multiple pursuers and a single evader, and (3) a single pursuer and multiple evaders. Compared to variational methods, this reachable set strategy leads to a tractable formulation even when there are state and control constraints. The efficacy of the strategy is demonstrated in three numerical simulations for a constellation of satellites in close proximity in low earth orbit. Full article
(This article belongs to the Special Issue Convex Optimization for Aerospace Guidance and Control Applications)
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17 pages, 417 KiB  
Article
Convex Optimization-Based Techniques for Trajectory Design and Control of Nonlinear Systems with Polytopic Range
by Olli Jansson and Matthew W. Harris
Aerospace 2023, 10(1), 71; https://doi.org/10.3390/aerospace10010071 - 10 Jan 2023
Viewed by 1659
Abstract
This paper presents new techniques for the trajectory design and control of nonlinear dynamical systems. The technique uses a convex polytope to bound the range of the nonlinear function and associates with each vertex an auxiliary linear system. Provided controls associated with the [...] Read more.
This paper presents new techniques for the trajectory design and control of nonlinear dynamical systems. The technique uses a convex polytope to bound the range of the nonlinear function and associates with each vertex an auxiliary linear system. Provided controls associated with the linear systems can be generated to satisfy an ordering constraint, the nonlinear control is computable by the interpolation of controls obtained by convex optimization. This theoretical result leads to two numerical approaches for solving the nonlinear constrained problem: one requires solving a single convex optimization problem and the other requires solving a sequence of convex optimization problems. The approaches are applied to two practical problems in aerospace engineering: a constrained relative orbital motion problem and an attitude control problem. The solve times for both problems and approaches are on the order of seconds. It is concluded that these techniques are rigorous and of practical use in solving nonlinear trajectory design and control problems. Full article
(This article belongs to the Special Issue Convex Optimization for Aerospace Guidance and Control Applications)
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30 pages, 6319 KiB  
Article
Convex Optimization for Rendezvous and Proximity Operation via Birkhoff Pseudospectral Method
by Zhiwei Zhang, Dangjun Zhao, Xianbin Li, Chunyang Kong and Ming Su
Aerospace 2022, 9(9), 505; https://doi.org/10.3390/aerospace9090505 - 09 Sep 2022
Cited by 6 | Viewed by 1886
Abstract
Rapid and accurate rendezvous and proximity operations for spacecraft are crucial to the success of most space missions. In this paper, a sequential convex programming method, combined with the first-order and second-order Birkhoff pseudospectral methods, is proposed for the autonomous rendezvous and proximity [...] Read more.
Rapid and accurate rendezvous and proximity operations for spacecraft are crucial to the success of most space missions. In this paper, a sequential convex programming method, combined with the first-order and second-order Birkhoff pseudospectral methods, is proposed for the autonomous rendezvous and proximity operations of spacecraft. The original nonlinear and nonconvex close-range rendezvous problem with thrust constraints and no-fly zone constraints is converted into its convex version by using the sequential convexification techniques; then, the Birkhoff pseudospectral method is used to transcribe the dynamic constraints into a series of linear algebraic equality constraints, in other words, a convex second-order conic programming problem with a relatively small condition number. Thus, the resulting problem can be accurately and efficiently solved by a convex solver. The simulation results indicate that the proposed methods, especially the second-order Birkhoff pseudospectral method, have obvious advantages over other methods in computational efficiency and sensitivity. Full article
(This article belongs to the Special Issue Convex Optimization for Aerospace Guidance and Control Applications)
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